## THERMAL SCIENCE

International Scientific Journal

### NON-DIFFERENTIABLE FRACTIONAL ODD-SOLITON SOLUTIONS OF LOCAL FRACTIONAL GENERALIZED BROER-KAUP SYSTEM BY EXTENDING DARBOUX TRANSFORMATION

**ABSTRACT**

In this paper, a local fractional generalized Broer-Kaup (gBK) system is first derived from the linear matrix problem equipped with local space and time fractional partial derivatives, i.e, fractional Lax pair. Based on the derived fractional Lax pair, the second kind of fractional Darboux transformation (DT) mapping the old potentials of the local fractional gBK system into new ones is then established. Finally, non-differentiable frcational odd-soliton solutions of the local fractional gBK system are obtained by using two basic solutions of the derived fractional Lax pair and the established fractional DT. This paper shows that the DT can be extended to construct non-differentiable fractional soliton solutions of some local fractional non-linear evolution equations in mathematical physics.

**KEYWORDS**

PAPER SUBMITTED: 2022-05-01

PAPER REVISED: 2022-06-04

PAPER ACCEPTED: 2022-06-14

PUBLISHED ONLINE: 2023-04-08

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